In an internal combustion engine having electrohydraulic valve control, a type of which is described, for example, in published German patent document DE 198 26 047, fluid under high pressure, e.g., hydraulic oil, is supplied to the electrohydraulic valve actuators for operating the gas exchange valves, and, at the same time, fluid under low pressure is carried off from the valve actuators and fed back to a fluid reservoir. The valve actuators each have a double-acting working cylinder having an operating piston, which is shiftable inside the cylinder, connected to the associated gas exchange valve, which subdivides the working cylinder into two hydraulic working chambers. By appropriate pressure control of the fluid in the working chambers using two electrical control valves, e.g., 2/2-way solenoid valve, the operating piston is shifted into one or the other direction, and thereby the associated gas exchange valve is opened in a defined manner or closed completely.